for \(|x|>R_0\) , with \(R_0>0\)  large enough, and then \(u\)  is superharmonic at infinity. From the Hadamard three spheres theorem [1]}, this implies that the function \(m(r):= \min \limits _{|x|=r} u(x)\)  satisfies
\(m(r) \ge \frac{m(r_1)\big (r^{-2}-r_2^{-2}\big ) + m(r_2)\big ( r_1^{-2}- r^{-2}\big )}{r_1^{-2}- r_2^{-2}} \qquad \forall R_0 < r_1 < r < r_2.\) 
